Mathematical Model Of Process Research Articles

A method for predicting methane production from anaerobic digestion of kitchen waste under small sample conditions.

Anaerobic digestion (AD) has the great potential to treat organic waste and achieve remarkable results effectively. However, it is very tough to establish an accurate mechanistic model for this process. Data-driven modeling technology has opened a new door to solving this problem. While when the sample set is small, traditional data-driven modeling methods are often powerless. In this paper, an effective method is proposed for data-driven high-precision modeling in small sample scenarios. A time series generative adversarial network (TimeGAN) is first utilized to augment the original high-quality small-sample data collected during the AD methane production. A novel hybrid kernel extreme learning machine (HKELM) is then designed to form a better structure of the data-driven model, whose regularization coefficient C0 is optimized by the sparrow search algorithm (SSA). Finally, this semi-finished model (SSA-HKELM) is trained by the augmented data to form the final mathematical model (TimeGAN-SSA-HKELM) for the AD methane generation process. Comparative experiments of the methane daily production prediction error haveverified the effectiveness of the method, which can be extended to other similar small sample data-driven modeling scenarios.

SIMULATION THE PROCESSES OF ORGANIC MATERIALS DESTRUCTION AND COMBUSTION PROCESSES CONDITION OF FIRE INTENSEICATION

Problem statement. The rapid occurrence and development of fires are caused by the occurrence of combustible materials and structures in their focus. This complicates, and in some cases makes impossible, effective firefighting, evacuation, and rescue of people and property. In order to correctly assess fire resistance, effectively increase fire resistance, and change the flammability of materials, it is necessary to study the materials burning process. The purpose of the article. To study of the combustion of easily dispersible substances and the development of gaseous reactions and their combination using the example of wood combustion. Methods. We use mathematical modeling of combustion and destructive processes under the high temperatures, taking into account the rules of thermodynamics. Research results. The conducted analysis showed that the selection of the main stages in the simulation of wood combustion is much less developed than in the case of the combustion of gas systems. It is especially difficult to do this to describe the combustion of wood, on the surface of which there is an interaction of masses (and heat) during the combustion of individual components, and the size of the front surface per unit cross-section of the sample may also change over time. Therefore, the definition of the main stage in wood burning should be used mainly in the qualitative analysis of the process, and quantitative models of wood burning should be built, if possible, taking into account all the determining factors characterizing the phenomena. Scientific novelty. For the first time, on the basis of the modeling of organic material combustion is proposed. We determine the patterns of destructive processes, which, depending on the temperature, have common patterns of qualitative and quantitative characteristics. The chemical phasing and its connection with the physical phasing of the transformation of combustible organic materials dispersed in the surface layer with the overall thermal effect of the combustion wave were determined. Practical value. The identification of stages during the wave burning of wood allows for a qualitative display of processes depending on the spatial zone and its distance from the gas zone, which allows predicting the development of protective means of organic materials against combustion.

Creating Fuzzy Models from Limited Data

The design of experiments is a methodological approach in which measurement experiments are carefully planned to obtain highly informative data. This paper addresses the challenge of constructing mathematical models for complex nonlinear processes when the available measurement data have low information content. This problem often arises when data are collected without the guidance of an experimental modeling expert. We examine two practical examples to illustrate this issue: a textile wastewater decolorization process and atmospheric corrosion of structural metal materials. In both cases, the measured data were insufficient to construct highly accurate models. It is, therefore, necessary to make a trade-off between model complexity and accuracy by adapting modeling techniques to work effectively with the limited data available. The main aim of the paper is, therefore, to focus on simple but effective techniques that allow as much information as possible to be extracted from low-quality measurements and to maximize the usefulness of the model for its intended purpose.

Improvement of mathematical model for catalytic reforming process with a stationary catalyst layer

Improvement of mathematical model for catalytic reforming process with a stationary catalyst layer

Mathematical Modeling of the Heat Transfer Process in Spherical Objects with Flat, Cylindrical and Spherical Defects

This paper proposes a method for determining the optimal parameters for the thermal testing of plant tissues of fruits and vegetables containing surface and subsurface defects in the form of areas of plant tissues with different thermophysical characteristics. Based on well-known mathematical models for objects of predominantly flat, cylindrical and spherical shapes containing flat, spherical and cylindrical regions of defects, numerical solutions of three-dimensional, non-stationary temperature fields were found, making it possible to measure the power and time of the thermal exposure of the sample surface to the radiation from infrared lamps using the finite element method. This made it possible to ensure the reliable detection of a temperature contrast of up to 4 °C between the defect and defect-free regions of the test object using modern thermal imaging cameras. In this case, subsurface defects can be detected at a depth of up to 3 mm from the surface. To determine the parameters of mathematical models of temperature fields, such as thermal conductivity and a coefficient of the thermal diffusivity of plant tissues, a new method of a pulsed heat flux from a flat heater is proposed; this differs in the method of processing experimental data and makes it possible to determine the required characteristics with high accuracy during the active stage of the experiment in a period not exceeding 1–3 min.

К уточнению понятий «концепт» и «концептология» (Подсказка читателя)

The “concept” as a basis for the construction of the science “conceptology” is studied. The question of the concept structure, the language of its description and the possibility of using mathematics for this purpose is discussed. Conceptology is considered as a scientific understanding of political reality in interrelation with social and natural reality. The characteristics of the spaces related to the mentioned types of reality and peculiarities of their conjugation in the concept structure are analyzed. The reasons for the ineffectiveness of mathematical modeling of social processes in the era of 1970s and the chances of success of modern researchers are analyzed. It is concluded that it is possible to develop the science of politics to a level comparable in its rigor, clarity and accuracy of forecasting with physics or mathematics.

Аналіз впливу на прохідність автобронетанкової техніки конструктивних факторів та методика її збільшення шляхом автоматичного регулювання тиску повітря в шинах коліс

The purpose of the study is to analyze and determine the influence of various factors on the patency of armored vehicles (AMT) operated by the National Guard of Ukraine. Determination of the change in patency during the movement of AMT in different road and climatic conditions. Analysis of static and dynamic loads, which are characteristic of AMT movement over rough terrain, and their impact on the efficiency of the vehicle. The theoretical component of the study was carried out using mathematical modeling of the work process of regulating the air pressure in tires of AMT wheels, using the example of changes in the characteristics of adhesion coefficients with the supporting surface and rolling resistance depending on the change in pressure and load on the tires of the wheels when the AMT is moving off-road. As a result of mathematical modeling, the dependences of air pressure in tires of AMT wheels were obtained, depending on the coefficient of rolling resistance and the load on each of the wheels. Which, in turn, makes it possible to move to a sufficiently complete mathematical modeling of the movement of AMT on off-road, taking into account the reference cross-country ability. In the process of theoretical research, the structural parameters of the impact on the patency of AMT were analyzed quite completely, and a generalized comparative indicator of the patency parameters of vehicles was proposed. When analyzing it, it was found that the AMT tire and, specifically, the change in air pressure in it, have a significant impact on the bearing capacity. The authors propose to use the following evaluation criteria as criteria for assessing the efficiency of the passability when driving on deformable surfaces: a generalized comparative indicator of the parameters of the passability of vehicles. As a result of consideration of which, a significant influence on the patency parameters of the tires and directly the air pressure in them was established. Regulation and change of the air pressure in the tires of the wheels depending on the change in the coefficient of rolling resistance as well as the change in the load on each wheel, which are the ratio of the work that is spent on the traction force when overcoming different degrees of heaviness of the resistance of the supporting surfaces with the effect of deformation. And the load that falls on each of the AMT wheels allowed us to draw conclusions about the improvement of the regular tire pressure regulation system (RPRS) of the wheels.

THE AIRCRAFT ENGINE PROPELLER MAIN CHARACTERISTICS DETERMINATION IMPROVED METHOD

An improved method of the fixed and variable pitch propeller aerodynamic characteristics determining that based on the vortex theory is presented. It is shown that the design of propellers has it`s peculiarities, it does not take into account a number of factors that affect the propeller operation to one or another degree. This actualized the special purpose unmanned aerial vehicles engines propellers aerodynamic characteristics calculating methodology improvement. Since the use of the propeller profiles performances in the design requires the air compressibility correction introduction already after the selection of the propeller, that complicates the design, therefore the mathematical model of the variable-pitch propeller working process has been improved based on the profile model with the correct consideration of the Mach and Reynolds numbers influence on the aerodynamic characteristics of the air screw. This advantage of the developed airfoil model allows the design and verification of a subsonic propeller for ground and flight operations. Methods of design and verification calculations of propeller blades are presented. Verification of the improved methodology was carried out by comparing calculated data with known experimental data. The reliability of the improved aircraft engine propeller main performances determination methodology is substantiated by the correct application of the numerical and experimental methods of aerodynamics, the consistency of theoretical provisions with experimental data. The satisfactory coincidence of the calculated data obtained by the improved method of the engine propeller main performances determination allowed us to draw a conclusion concerning its efficiency. The improved technique for the main performances of an aircraft engine propeller determination does not require knowledge on the propeller profiles aerodynamic characteristics from which the blade is drawn, since these characteristics are calculated based on known geometric data, taking into account the Mach and Reynolds numbers. This allows you to design and build a subsonic propeller of both fixed pitch and variable pitch.

Analysis of the privacy-performance tradeoff of reference testing in Forensic Investigative Genetic Genealogy.

During an investigation using Forensic Investigative Genetic Genealogy, which is a novel approach for solving violent crimes and identifying human remains, reference testing-when law enforcement requests a DNA sample from a person in a partially constructed family tree-is sometimes used when an investigation has stalled. Because the people considered for a reference test have not opted in to allow law enforcement to use their DNA profile in this way, reference testing is viewed by many as an invasion of privacy and by some as unethical. We generalize an existing mathematical optimization model of the genealogy process by incorporating the option of reference testing. Using simulated versions of 17 DNA Doe Project cases, we find that reference testing can solve cases more quickly (although many reference tests are required to substantially hasten the investigative process), but only rarely (<1%) solves cases that cannot otherwise be solved. Through a mixture of mathematical and computational analysis, we find that the most desirable people to test are at the bottom of a path descending from an ancestral couple that is most likely to be related to the target. We also characterize the rare cases where reference testing is necessary for solving the case: when there is only one descending path from an ancestral couple, which precludes the possibility of identifying an intersection (e.g., marriage) between two descendants of two different ancestral couples.

A Physical Insight into Computational Fluid Dynamics and Heat Transfer

Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article represents a derivative-free approach for the mathematical modelling. The proposed approach for CFD and numerical heat transfer is based on the conservation and phenomenological laws, and physical constraints on the minimum problem-dependent spatial and temporal scales (for example, on the average free path of molecules and the average time of their collisions for gases). This leads to the derivative-free governing equations (the discontinuum approximation) that are very convenient for numerical simulation. The theoretical analysis of governing equations describing the fundamental conservation laws in the continuum and discontinuum approximations is given. The article demonstrates the derivative-free approach based on the correctly defined macroparameters (pressure, temperature, density, etc.) for the mathematical description of physical and chemical processes. This eliminates the finite-difference, finite-volume, finite-element or other approximations of the governing equations from the computational algorithms.

A Physical Insight into Computational Fluid Dynamics and Heat Transfer

Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article represents a derivative-free approach for the mathematical modelling. The proposed approach for CFD and numerical heat transfer is based on the conservation and phenomenological laws, and physical constraints on the minimum problem-dependent spatial and temporal scales (for example, on the average free path of molecules and the average time of their collisions for gases). This leads to the derivative-free governing equations (the discontinuum approximation) that are very convenient for numerical simulation. The theoretical analysis of governing equations describing the fundamental conservation laws in the continuum and discontinuum approximations is given. The article demonstrates the derivative-free approach based on the correctly defined macroparameters (pressure, temperature, density, etc.) for the mathematical description of physical and chemical processes. This eliminates the finite-difference, finite-volume, finite-element or other approximations of the governing equations from the computational algorithms.

A Mathematical Modeling of Computer Numerical Control Skiving Process for Manufacturing Helical Face Gears Using Sensitivity Matrix Combined With Levenberg–Marquardt Algorithm

Abstract Currently, numerous studies have applied gear skiving processes to produce face gear. However, there remains a significant challenge in achieving a flexible computing model for manufacturing a precise tooth surface for face gear. This study proposes a novel mathematical model that combines the cutter modification method and computer numerical control (CNC)-axis motion modification methods within a unified “closed-loop optimization.” This approach aims to enhance the tooth surface accuracy of skived helical face gears by determining optimal coefficients. Applying the Levenberg–Marquardt algorithm and sensitivity matrix enables the calculation of new polynomial coefficients, ensuring the attainment of gear surfaces with an accuracy grade of B6 (according to the ANSI/AGMA 2009-B01 standard) for each target surface. The proposed methodology involves the generation of a helical skiving cutter using a corrected rack. Subsequently, the cutting path on the CNC machine is optimized by incorporating additional motions expressed in polynomials. A comprehensive skiving simulation is conducted to achieve the desired face-gear surface, which is corrected by specified polynomial coefficients. The proposed model is validated through numerical and machining simulations using vericut software. The results affirm the practicality and efficacy of our approach in achieving the desired accuracy in producing helical face gears through power skiving processes.

Shortcut model to evaluate the performance of continuous preferential crystallization for conglomerates forming chiral systems

The separation of two enantiomers of a chiral molecule is one of the most difficult tasks for separation technology. Among the available methods, Preferential Crystallization (PC) offers a relatively simple and efficient possibility to separate pairs of enantiomers of conglomerate forming chiral systems. To estimate the potential and to design PC processes, mathematical process models are required. Recently, a short-cut model (SCM) was developed which was found capable to predict the course of batch-wise operated PC until nucleation of the unseeded counter-enantiomer terminates the exploitable production period. In this paper the SCM is reformulated in a dimensionless way and extended to describe also more productive continuous operation of PC. Characteristic dimensionless numbers are demonstrated to be instructive to evaluate effects of system specific kinetic parameters and to identify suitable operating conditions. The sensitivity of the continuous PC process with respect to the most relevant model parameters is investigated based on simulation results. Finally, the role of the SCM in the workflow of designing continuous PC processes is summarized.

Mathematical modeling and performance evaluations of a wood drying process using photovoltaic thermal and double-pass solar air collectors

This research conducts a novel and complete 4E assessments and introduces an innovative method for examining solar wood drying systems. The software TRNSYS and MATLAB programming are combined to simulate and create a numerical program. This novel combination allows for a thorough examination that goes beyond conventional assessments of wood drying. The aim is to evaluate the effectiveness of a solar wood dryer using two different collectors, a double-pass and a photovoltaic thermal collectors, in terms of four key aspects: energy, exergy, economic, and environmental. Further, the drying process was investigated under various climates in three African cities (Errachidia, Dakar, and Nouakchott). The moisture content of wood was reduced from 74% to 12% in the three cities. Elaborate simulations were performed and the results were confirmed by experimental validation, using methods including Mean Absolute Error, Mean Relative Error, and Root Mean Square Error.The primary findings of this study are the following: In the double-pass dryer, the drying time required in Errachidia, Dakar, and Nouakchott was 139h, 189h, and 170h, respectively. Whereas in the photovoltaic thermal dryer, it needed 192h in Errachidia, 210h in Dakar, and 189h in Nouakchott. Further, using photovoltaic thermal, the dryer exhibited superior exergy efficiency compared to the use of double pass collector. Photovoltaic thermal collector reduces yearly CO2 emissions by an average of 54.87, 66.2, and 44.11 tonnesCO2 in Errachidia, Dakar, and Nouakchott, respectively. In contrast, double pass collector reduces CO2 emissions by an average of 38.49, 57.9, and 38.56 tonnesCO2 in Errachidia, Dakar, and Nouakchott, respectively, throughout the year. Further, the solar dryer, using double pass collector, has a shorter payback time than using photovoltaic thermal collector, indicating a quicker economic return.

Применение принципа Понтрягина для оптимального отключения энергетического ядерного реактора

The theory of optimal control is based on two approaches, the dynamic programming method (Bellman equation) and Pontryagin maximum principle. Pontryagin maximum principle is applied in the physics of nuclear reactors when optimizing various transient processes. The mathematical justification of this theory is based on the elements of convex analysis, which is not used by physicists and engineers, so the physical issues are less studied in scientific literature. The subject of the study is a nuclear power reactor of the WWER type. The problem of minimizing its shutdown time, bypassing the iodine pit is solved and it is possible to start up the reactor at any moment after its shutdown. Analytical and numerical methods are used. The paper considers an example of applying the maximum principle for optimal control of the process of shutting down a nuclear reactor bypassing the iodine pit. A physical mathematical model of the Pontryagin principle is formulated. The process of optimal control of reactor shutdown for large and small reactivity margins is justified and calculated. Pontryagin principle does not contain an algorithm to find an optimization process; the stages of the process must be selected based on physical considerations, but these stages must satisfy the specified principle. Based on the Pontryagin principle, the results of the study make it possible to draw up a step-by-step action plan when shutting down a WWER-type reactor with any value of the reactivity margin and its switching is possible at any time after the transition process, which avoids downtime. The proposed plan can be used both in mathematical modeling of transient processes in a reactor and in reactor control systems to improve its controllability and, consequently, to improve safety.

Anthropogenic impact on agricultural landscapes of the Akmola region of the Republic of Kazakhstan

The relevance of research topic is confirmed by the presence of environmental problems of steppe land use and the need for its rationalization. The article examines the issues of ecological stability of agrolandscapes of the steppe zone in agricultural circulation and determines environmental and economic damage that occurs when their functioning is disrupted. The goal is to assess the degree of anthropogenic influence when using agricultural landscapes based on the example of the Akmola region. The content of research topic determined the choice of the following methods: historical, logical, statistical, system analysis, graphic modeling. Results - taking into account factors that destabilize the landscape-ecological balance, ecological zoning was carried out in the region, the degree of stability of steppe agricultural landscapes under anthropogenic influence was determined, based on mathematical model of erosion process, intensity of washout was calculated, environmental and economic losses arising in connection with violation were indicated, self-regulation of landscapes, environmental protection (antierosion) measures have been developed. The amount of residual flushing after they are carried out characterizes the effectiveness of reducing the water flows. Conclusions - field agrolandscapes of agricultural enterprises of the Akmola region, specializing in production of crop products, can be classified as anthropogenically disturbed with low degree of environmental stability, which is due to the significant plowing of their territory. One of the main factors of environmental destabilization in steppe agricultural entities is the spread of water erosion on slope arable land, environmental damage from which is confirmed by the loss of soil layer. The proposed measures to support landscape environmental stability can be applied when planning the use of land resources and developing on-farm land management projects.

Influence of connecting a new gas pipeline to the operating gas pipeline on the flow rate of production wells

In some cases, it is necessary to connect new line to the pipeline. From this point of view, in the presented work, serious changes occurring in the pipeline as a result of connecting a new gas pipeline to the operating gas pipeline are investigated. The changes occurring in the pipeline are transmitted to the formations, which causes a violation of the stable operation of the wells in the initial period. After a certain period of time, the dynamic processes formed in the system as a result of changes in the transport line become stationary. From this point of view, it is of great practical importance to consider the stationary state of the processes occurring in the system. Therefore, in the presented work, as a result of the addition of a new line to the pipeline, the change in the production of gas wells in stationary regime conditions is studied. The effect of these changes on the operating mode of the wells, the effect on the change in production of operational wells is studied. Taking into account the interaction of the layer-pipeline system, a mathematical model of the movement process of gas and gas-liquid mixture is established, using the equations of motion and continuity, the resulting system of related differential equations is solved. With the help of the obtained formulas, the pressure drop and production reduction for each well are calculated during the connection of the new line. Numerical calculations are performed using various practical values of system parameters and the obtained results are analyzed. Keywords: production; layer; pressure; pipeline; stationary state; gas-liquid mixture; motion and continuity equation.

Analysis of the sintering process of the sintering charge in a high layer. Report 1. Fuel combustion and dissociation of limestone

Communication 1 provides a brief overview of theoretical works on the creation of mathematical models of the sintering process, ranging from simplified balance models to the three-dimensional dynamic model. A modern three-dimensional mathematical model is adapted from industrial data on the agglomeration of a sinter mix in a bed 700 mm high with a bed of sinter at the sinter plant No. 5 of PJSC “MMK”. Changes in the device circuit diagram of sinter plan, the actual temperature of the mix, segregation of fuel along the height of the bed, the mode of intensive ignition of the mix in the ignition hearth with diffusion burners, the unevenness of the sintering process across the width of the pallets, additional heating of the bed after the hearth with air from a linear cooler, the actual degree of throttling of the vacuum chambers of the sinter machine, heat exchange in pallets are taken into account. The process of a combustion zone of solid fuel formation under the ignition hearth has been analyzed, and an increase in its height during the sintering process in a high bed has been established, that due to the segregation of mix and fuel along the height of the bed and the consumption of oxygen for the oxidation of FeO above this zone. The processes of limestone dissociation and melting of the mix zones formation and their development during the sintering process are considered

Mathematical understanding (hermeneutic aspects of educational activities)

The article discusses the issues of mathematical understanding as an educational practice of identifying the algorithmic meanings of mathematical (mathematized) educational texts. The hermeneutic orientation towards following the “guiding thread of language” (G.-G. Gadamer), as it is shown, cannot be narrowed to the attitude towards natural languages inherent in humanitarian educational practices. The “common place” of mathematical understanding in educational practices is: some of created languages (of scientific communication) being consolidated around the mathematical installation are not reducible to its sign universality or educational generalizations. But it often turns out to be outside the field of view of practicing teachers, in a didactically abstract position. The article substantiates the possibility of rehabilitating the hermeneutic attitude in mathematical education in connection with its development and strengthening in understanding the prerequisites for the algorithmic solution of mathematical problems (the need for additional information, non-standard solution techniques, transfer of educational goal setting to the area of interdisciplinary relationships or life experience, etc.). The author shows and comments on the effectiveness of the hermeneutic approach in mathematics education using examples of solving problems in algebra, geometry and in constructing mathematical models of various physical processes.

Частная полумарковская модель как инструмент снижения сложности задачи оценивания устойчивости функционирования элементов информационной инфраструктуры, подверженной воздействию угроз

Decision-making on information infrastructure (II) security for its sustainable functioning in the face of threats requires a tool to assess the sustainability of its individual elements. The application of the semi-Markov model to assess the stability of the functioning of elements of II exposed to threats in a direct setting is associated with the increasing complexity of the description of the object of delineation (parametric space) in step progression from the number of the considered impacts, which reduces its practical significance. However, no studies have been found in the scientific literature to reduce the complexity of the semi-Markov model. The article presents an approach to reducing the complexity of modeling by adopting correct assumptions when forming the initial data. Given the conditions under which it is possible to take a series. It was a cost to limit the applicability of the model by significantly reducing the complexity of the modelling. The problem statement and the modified transition graph are given. The novelty of the problem statement is to take into account the limitations on the available resources for the restoration of functionality of the element. To explain the physical essence of the modeling process, a thought experiment with a model is introduced. To solve the problem, the following methods were used: a) expert methods for extraction of initial data; b) mathematical models of private semi-Markov processes; c) methods of transformation of Laplace; r) methods of planning of experiment. Illustrative examples and graphs accompany the task sequence demonstration. As a result of the experiment, the regularities of the studied process, the existence of which was proved formally. As a result of the experiment, the regularities of the studied process were revealed, the existence of which was officially proved. The results of the study broaden knowledge about the application of methods of Markov processes to assess the stability of the functioning of AI elements in relation to the conditions of the impact of threats.